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We ranked the CV of genes in each dataset and constructed a matrix of ranked CV to datasets.
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Let X be an N× k matrix of ranking data such that x ij represents the rank of item j assigned by judge i, centered by the overall mean rank, i.e., (k + 1)/2.
Letting, should be a positive semidefinite matrix of rank.
I N Identity matrix of rank N. T, H Transpose and Hermitian transpose.
Let A be an (mtimes n) real (complex) matrix of rank r.
where I is the identity matrix of rank M and SNR is the signal-to-noise ratio.
Let (U_{2}) and V contain exactly one non-zero element such that the non-zero element in (U_{2}) is in a different column to the non-zero element in V. Let W=J_{2}+U_{2}^V-V^U_{2}. (4.6) Then (U_{2}^V) and (V^U_{2}) are (8times8) matrices of rank 1, (U_{2}^V-V^U_{2}) is an (8times8) matrix of rank 2 and W is an (8times8) matrix of rank at least 6.
If the seismic data consist of a complex events, the associated Hankel matrix of the data is a matrix of rank a (Hua 1992).
As the DCT basis functions change only slowly with, SCEN2 yields a matrix with nearly identical rows, so it behaves like a matrix of rank 1.
where I M denotes an M × M identity matrix, H denotes the complex conjugate transpose, and R s s is the source covariance matrix of rank K.
One then forms the 2 × 2 symmetric matrix of rank one T 0 = ∇ I σ 1 ( ∇ I σ 1 ) T, where T indicates the transpose of a vector.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com